# Research on Multi-Objective Optimization Method for Hydroforming Loading Path of Centralizer

## TL;DR

This study explores how to optimize the pressure and feed paths during centralizer hydroforming to achieve uniform wall thickness and avoid defects.

## Contribution

The paper introduces a multi-objective optimization framework combining several algorithms with LS-DYNA for hydroforming process design.

## Key findings

- NSGA-II, NCGA, and AMGA successfully generated optimized loading paths.
- NSGA-II and AMGA produced larger sets of higher-quality Pareto solutions.
- MOPSO showed premature convergence and yielded inferior results.

## Abstract

During centralizer hydroforming, internal pressure and axial feed critically influence the forming outcome. Insufficient feed causes excessive thinning and cracking, while excessive feed causes thickening and wrinkling. Achieving uniform wall thickness necessitates careful design of the pressure and feed curves. Using max/min wall thickness as objectives and key control points on these curves as variables, the study integrated Non-dominated Sorting Genetic Algorithm (NSGA-II), Multi-Objective Particle Swarm Optimization (MOPSO), Neighborhood Cultivation Genetic Algorithm (NCGA), and Archive-based Micro Genetic Algorithm (AMGA) with LS-DYNA to automatically optimize loading paths. The results demonstrate the following: ① NSGA-II, NCGA, and AMGA successfully generated optimized paths; ② NSGA-II and AMGA produced larger sets of higher-quality Pareto solutions; ③ AMGA required more iterations for satisfactory Pareto sets; ④ MOPSO exhibited a tendency towards premature convergence, yielding inferior results; ⑤ Multi-objective optimization efficiently generated diverse Pareto solutions, expanding the design space for process design.